In work apparatus such as motor-driven chain saws, cutoff machines or the like driven by an internal combustion engine, the air-cooled engine is disposed in a housing and is cooled by a flow of cooling air. Especially in handheld portable work apparatus, a compact configuration is desired in order to obtain a high level of manipulability. With the compact configuration, the drive and the ancillary components are crowded into a housing as small as possible. This leads to considerable temperature problems because of the engine since, for example, a fuel tank mounted in the housing is placed close to the cylinder or to the exhaust-gas muffler. The crowded configuration can in addition lead to overtemperatures thereby leading to damage at the cylinder. For this reason, an adequately high air throughput for conducting away the heat must be generated by a cooling air fan dimensioned to have the appropriate size. A large-dimensioned cooling air fan not only needs a correspondingly large amount of driving energy, which is then not available at the tool of the work apparatus, but also, the air-cooled fan must be large so that the desired reduced size of the work apparatus itself is not achieved.